The Cantor Set

Alexander Yu. Shibakov

The Ural University, Ekaterinburg

Andrzej Trybulec

Warsaw University, Bialystok

Summary.

The aim of the paper is to define some basic notions of the theory
of topological spaces like basis and prebasis, and to prove their
simple properties. The definition of the Cantor set is given in terms
of countable product of $\{0,1\}$ and a collection of its subsets
to serve as a prebasis.

The present work had been completed while the first author's visit to
Bia{\l}ystok in winter 1994--95.